This activity has benefited from a review and suggestion process as a part of an activity development workshop.

This activity has benefited from input from faculty educators beyond the author through a review and suggestion process as a part of an activity development workshop. Workshop participants were provided with a set of criteria against which they evaluated each others' activities. After the review, the authors developed a plan for revising their activities based on the feedback they received from their peers. To learn more about this review process, see http://serc.carleton.edu/quantskills/review_processes.html#2006.

This page first made public: Jul 20, 2006

Summary

This is an in-class, group activity for a physical geology introductory course based on a simplified hypothetical mining scenario, with the main scope to practice students' problem-solving abilities and cooperative quantitative learning. Students collect specific gravity measurements on sets of mineral samples and apply them to figure out the total metal (iron) content of a given shape of the ore body (quarry bench) of variable ore grade. The experiments, data collecting and problem solving are performed in teams. A short, individually written report may follow as homework.

Learning Goals

Concepts:

Natural resources, consumption, and waste

relation between volume, mass, and density

density of solids as a function of mineral (chemical) composition and porosity.

Higher order quantitative skills:

problem solving;

measurement, data tabulating and data analysis;

spatial visualization;

model development: reducing a complex shape to a set of simple geometrical shapes (cone, cylinder, cubes);

critical thinking.

Context for Use

This activity is designed for an introductory, lower level Physical Geology class with emphasis on quantitative learning through group work. The level of math literacy of the students is variable, but generally low. It is designed for an average class size (31-70 students). It is a two-hour activity, finalized with a short written report. The activity may be inserted at the end of a section on minerals or as part of a section on mineral and energy resources. The students should be familiar with the chemical composition of a mineral and the use of the periodic table.

Description and Teaching Materials

Note: This activity is under construction (the activity has not yet been tested in the classroom).
The main questions to answer are A) how much metal was produced and B) how much waste resulted from quarrying a given portion of an ore body of somewhat complex geometric shape and variable composition. The activity includes

a volume estimate of the ore body based on a given topographic map,

density measurements of two minerals,

calculating density of ore function of given ore grade (given percentage of the two minerals),

deriving the total metal content of the ore body, number of cars that can be built from this ore, and

the volume of waste derived from the ore processing, taking into account the porosity of the crushed waste.

The students are provided with a topographic map that includes a quarry, and some representative sketches/vertical profiles. Other materials: two minerals of contrasting density (possibly a set of 3 different fragments per group for multiple measurements): the ore mineral (magnetite) and the waste mineral (quartz); scale for measuring specific gravity (one per group); cup/beaker with water. Other pertinent information: ore compositions for each of the volumes; porosity and composition of the crushed waste.
The instructions in the handout will be kept to a minimum to encourage problem solving. Definitions and formulas provided: the specific gravity of a solid (weight in air divided by difference between weight in air and weight in water); approximation: specific gravity equals density; formulas of pertinent geometric volumes. Background information on quarrying an ore deposit, processing the ore, and disposing of the waste is also provided, with specific details from the mining operations from the Upper Peninsula of Michigan, including representative porosity and composition of the crushed waste material.
Based on the given information and materials, students design a strategy for solving the problem starting with designing an experimental set up to measure the specific gravity, to estimating the volume, calculating the weighted density of the ore, the total mass of the ore, the mass of magnetite within the ore, and the mass of iron. Using given values of porosity of the waste material and approximating it as pure quartz, they also calculate the volume of the waste that resulted from the quarry.

Teaching Notes and Tips

Note: This activity is under construction (the activity has not yet been tested in the classroom).

If this is the first time when multiple measurements are encountered in this course, this is an opportunity to introduce simple statistics and to show students how to evaluate measurement uncertainties.

Specific suggestions for the experiments: Students collect specific gravity measurements for the minerals magnetite and quartz three times and the average is calculated. The averages resulted from all groups are then reported on the blackboard so that the average specific gravity values can be calculated. A bar chart of all values for the two minerals is constructed so that the potential outliers are identified and eliminated and in order to contrast between the two minerals.

If students have not been previously exposed to problem-solving activities, a problem-solving worksheet (similar to Ken Heller's, add link) may be provided to structure their thinking path.

The activity may be followed by a group debate activity to discuss the economic, social, and environmental impact of re-vitalizing the iron mining in the Upper Peninsula. A scenario including role playing: Students will be divided in representatives of the mining company, union representatives, state representatives and Environmental Protection Agency.